Modeling Asymmetric Exchanges Between Clusters

A nonhierarchical clustering model is proposed here which jointly fits the symmetric and skew-symmetric components of an asymmetric pairwise dissimilarity matrix. Two similar clustering structures are defined depending on two (generally different) partitions of the objects: a “complete” partition fitting the symmetries (where all objects belong to some cluster) and an “incomplete” partition fitting the skew-symmetries, where only a subset of objects is assigned to some cluster, while the remaining ones may remain non-assigned. The exchanges between clusters are accounted for by the model which is formalized in a least squares framework and an appropriate Alternating Least Squares algorithm is provided to fit the model to illustrative real data.